The technique of stabilizing earth structures by incorporation of spaced flexible reinforcements in the earth mass has become well-established. The basic principles of this procedure were set out in British Patent No. 1039361 of Henri Vidal and a large number of structures of this kind have been build all over the world. The reinforcements stabilize the mass virtually completely by frictional forces, both between the reinforcements and the adjacent fill particles and between those particles and the remainder of the fill. The reinforcements are so spaced that such frictional forces are transmitted throughout the fill and tension generated in the reinforcements opposes significant horizontal movement of the fill particles.
The tensile strength of the reinforcements must be sufficient to withstand the horizontal forces generated by the weight of the fill and any loads placed thereon, such as a road and road traffic. In order to retain the elastic properties of the stabilized earth structure, it is necessary that any modified form of the reinforcement should be flexible, in order to retain frictional contact with the fill and accommodate earth movements. It has been found that an earth mass stabilized in this way can be built with vertical sides up to substantial heights and the earth behaves as a material having predetermined elastic properties capable of accommodating significant vertical settling movements without failure.
An unstabilized block of earth has a tendency to fail in the well known way first described by Coulomb along a plane from the foot of the block at an angle of .alpha.=.pi./4+.phi./2 (where .phi. is the angle of friction), normally about 63.degree. to the horizontal. The mass of earth above this plane is often termed the "Coulomb wedge" or "active wedge". In older techniques, where a vertical wall was required, this was provided by a relatively massive wall structure at the vertical face resisting overturning primarily by its weight. Using the techniques of British Patent No. 1069361, the vertical sides of the earth block merely need protection from erosion and are commonly provided with relatively thin cladding elements attached to the exposed ends of the reinforcements.
The reinforcements used in the technique of British Patent 1069361 are, most efficiently, strips but differently shaped reinforcements are possible provided they are capable of mobilizing frictional forces adequate to stabilize the mass. The strips or other reinforcements are generally incorporated in the fill in layers, the structure normally being built up by placing a layer of spaced strips on a flat compacted layer of earth, compacting a further layer of fill on top of the strips and placing a further layer of strips, this procedure being continued until the structure has reached the required height.
It is found that the presence of the reinforcements according to the Vidal technique changes the properties of the earth mass to the extent that the boundary of the active wedge is substantially nearer to the vertical face of the mass than in the case of unreinforced earth. Recent experiments have shown that, surprisingly, the position of the boundary of the active wedge, which is, in fact, the line of maximum tension in the reinforcements, runs almost parallel to the vertical face, except for the region near the foot of the structure. Thus it has been found that the boundary of the active zone lies, for the greater part of the structure, at a distance about 0.28 H (.+-.0.02 H) from the face (where H is the height of the structure).
In such a structure, the reinforcements have always had a length of at least 0.7 H which means that a length of reinforcement of at least 0.4 H extended beyond the active wedge into the resisting zone, i.e. the zone not liable to failure. In low or medium height walls, the length of the reinforcements is normally greater relative to height, e.g. 0.7 to 1.2 H, so that in such cases even more of the reinforcement lies in the resisting zone and simply serves to mobilize sufficient friction in the earth mass to resist movement of the stabilized active wedge. The surface area of reinforcement in contact with the fill is calculated to ensure that the reinforcements cannot be pulled out. Substantial safety factors are always applied, however, and it has not been previously appreciated how little of the length of the reinforcements lay in the active wedge.
The reinforcements have always been designed to present a substantially uniform frictional surface over their length. Typically these have been strips of stainless or galvanized steel, sometimes provided with transverse bars to increase frictional contact. When it is appreciated that only 0.3 H of the length of the reinforcement is required to stabilize the active wedge and the remainder, amounting to 0.4 H or more, functions simply to retain the reinforcement in the zone behind the active wedge, the retaining zone, it becomes possible to consider alternative ways of retaining the rearward parts of the reinforcements in the retaining zone which might result in savings of materials and hence costs. It will be appreciated that the length of the reinforcements contributes significantly to the cost of the structure both in terms of the material of the reinforcements and also the depth of fill which has to be moved and compacted to construct the wall.
It is believed that in any stablised earth structure, the flexible reinforcements should extend to a distance of least 0.45 H, preferably at least 0.5 H, in order maintain the desired characteristics of the mass except near the toe of the structure, where this could be reduced to 0.35 H or, more preferably, 0.4 H. Beyond a distance of 0.8 H however, it is now believed that frictional contact with the fill is unnecessary even in low walls.
As indicated above, previous designs have used reinforcements of length 0.7 H or greater and having uniform characteristics along their length. It has now been found possible to use shorter reinforcements, for example having a length of 0.65 H or less, more preferably about 0.5 H, provided the reinforcements are designed to ensure their retention in the retaining zone. It is thus possible to provide in the active zone, only sufficient frictional contact between the reinforcements and the earth to stabilize the active zone (with applied safety factors) while designing the rearward section of the reinforcements to resist pulling out of the retaining zone. This can be achieved by abandoning the concept of using reinforcements having uniform properties over their whole length and designing them with a stabilizing zone and a retaining zone having different frictional characteristics.
The point of maximum tension in such reinforcements will in general lie at a distance about 0.3 H from the front end. However, since the reinforcements will, in general, be designed to be used in building walls of various heights, the position of this point will vary according to the intended use. Nevertheless, it can be stated as a generalization that this point will normally lie in the central 1/3 of the length of the reinforcement. In considering the different frictional properties of the reinforcement on either side of the point of maximum tension it is therefore convenient to consider only the portions of the reinforcement on either side of this central section.